Subject: Is DFT ab initio?

From: JORGE <[email-masked]>
Date: 17 May 1995 00:29:51 -0600 (CST)

On The Question: Is DFT an ab initio method?

From my dictionary:
Theory        = System of rules and principles
Empirical     = Relying  on experimental information
Empirical     = Relying on experience [what about theoretical experience?]
Empirical     = Not Relying on theory
Approximation = very near, nearly correct

My understanding of a pure ab initio method is of any method that solves
(exactly or approximately) the Schrodinger equation, this means: using only
the principles of quantum mechanics and not using empirical or other
information extrapolated, interpolated, or transferred from other system(s).

Whether the method is a very rough approximation, is not going to eliminate
its ab initio character. In this sense, we have a spectrum of methods from the
very precise to the very inaccurate ones, forcing us to a trade-off because
the cost of the method is usually a direct function of its precision.

In general any practical computational method will be part ab initio
and part empirical in character, and it is not much subjective to determine
if a given method can be classified as ab initio, empirical or semiempirical.

The selection and use of a basis set is always based on experience;
whether, theoretical or experimental, one can always create or improve
a basis set based on how it behaved in earlier calculations. The basis set is
telling your method the spectral region to look for the solutions but it does
not constitute the solution itself.

A fully 100% analytical ab initio method would be limited to the solution
of the hydrogen-like atoms.

Another pure 100% ab initio, but nevertheless approximated method,
would be any of those variational-perturbational methods that solves
the helium-like atoms with about 15 figures!! of precision, and where
the basis set has been chosen with the only criteria of the lowest possible
energy.

Then come our standard ab initio methods, based on the central
field approximation, or HF-based methods (HF, MP, CC, CI, MRHF,...)
with several degrees of accuracy and several degrees of small empirical
(due to experiment or experience from earlier calculations) corrections
and truncations. We call all of them ab initio, and there is an implicit
understanding that this is where our definition of ab initio is settled.
Small corrections to those methods, like 10% correction to the ZPE do not
change our attitude toward the ab initio character of the
methods. There exists the accepted Gaussian2 theory where
corrections, not necessarily small, are made to the energies based on
precise experimental results.

Neither our ability to improve the level of theory would exclude
the ab initio character of a method.

Now to the question if DFT methods are ab initio:
First of all, you CAN derive DFT directly from the Schrodinger
equation even without recurring, as in HF methods, to the central field
approximation. The fact that a well defined but nowadays unsolvable
functional shows up can not exclude the ab initio character of
DFT. As in any of the ab initio methods above, approximations are
made. A classification could be done whether the functional was
derived using entirely first principles information or if it was
obtained by using experimental or other transferred information
Only on those cases where the functional is empirical, the 
particular DFT method can be catalogued as semiempirical.

Functionals like the local approximation, gradient approximation
are exact functionals (up to their order) and are obtained from
pure first principles arguments. The GGA of Perdew and Wang
for exchange-correlation, PW91, is strictly ab initio and there
are evidence that it performs as well as QCI and MP4 methods.
A predecessor to the PW91, the PW86, has been used with systems
containing up to transition metals with great success.
DFT methods can also be developed using fully numerical techniques, like in
Becke's Numol, eliminating the use of basis sets. Using this method
together with one of the ab initio functionals yields a 100% ab initio
procedure, i.e., more ab initio than any of the standard ones.

VERDICT:  We find DFT ab initio

Jorge Seminario
[email-masked]